I have a separate number pad on my laptop, and every version of Linux I've run seems to have a different method of activating numlock. As LXLE has become my primary Linux, I figured that I'd tell y'all how I got numlock working the way I wanted it to (all the time, including before login).

Here's how to get numlock on at boot/before login.

First, install the numlockx package:
sudo apt-get install numlockx

The /etc/lightdm/lightdm.conf file, which is the file you need in order for the below command to work, does not exist in a default installation of LXLE 16.04. So what we have to do is create and edit the file, which can be done in one step using this command:
sudo pluma /etc/lightdm/lightdm.conf

Add the following line to the file:
greeter-setup-script=/usr/bin/numlockx on

Save, exit, and reboot, and your numlock light should be on at boot.

Now, in case your numlock turns off after you login, here's what you need to do to turn it back on once you're logged into the system.

Menu Button => Control Menu => Settings => Default applications for LXSession
Click on the Autostart button
In the textbox next to the Add button, type /usr/bin/numlockx on
Click the Add button
Close the LXSession configuration window.

Once I closed that window, my numlock came on. If it doesn't immediately come on, then reboot.

These steps should turn your numlock on and keep it on all the time in 16.04.